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Tuesday, November 19, 2013


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"Hamlet is an incomplete object. He has all and only the properties ascribed to him in the play that bears his name. It is neither the case that he eats his eggs with hot sauce or that he doesn't. "

I don't follow this at all. I don't agree with the second sentence "He has all and only ….". Of course Shakespeare said that there was a person called ‘Hamlet’ who had certain properties (e.g. he said that Hamlet was a prince of Denmark. It doesn’t follow that there is someone who has or had such a property. For example, legend says that there was a horse called ‘Pegasus’ that flew. It doesn’t follow that there are or were flying horses.

And why does it follow that because someone fails us to provide us with certain information about something, that the information neither applies nor fails to apply? For example, I have never told you the colour of the front door of our house. It doesn’t follow that the door doesn’t have a colour.

It seems to me we have to buy an awful lot in your first premiss.

Good old London Ed, true to form, balks or rather baulks right at the git-go, rejecting (1)which I claimed is "surely true." Maybe I shouldn't have brought Shirley into it. In any case, I need a separate post to respond.

"Maybe I shouldn't have brought Shirley into it."

Maybe you shouldn't have brought Drew into it :)

Drew who?

I think your argument commits a modal fallacy. It has the following structure:

1. X
2. Necessarily, if X then Y.
3. So, necessarily, Y.

But this is invalid. Consider this argument:

3. It's raining today.
4. Necessarily, if it's raining today then the ground is wet.
5. So, necessarily, the ground is wet.

(3) & (4) are true; however, (5) is false. So, the argument is invalid. In order to make it valid, we'd have to say

(3*) Necessarily, it is raining today.

But, of course, (3*) is false. So, while we now have a valid argument, it's unsound.

I think the same goes for your argument. In its present form, it's invalid. To make it valid, we'd have to change your first premise to say

6. Necessarily, Hamlet is an incomplete object.

However, while the argument is now valid, it seems unsound; for certainly someone could give a complete description of Hamlet.

>>Drew who?

As in 'Shirley Drew' :)

And who might she be?

Pity you can´t speak czech, guys :-) we are lively discussing this very interesting topic at Daniel Novotny´s blog where he pointed to this text: http://poznamkypodcarou2012.blogspot.cz/2013/11/vallicella-fiktivni-individua-jako.html

I personally think that the correct reply is expressed in last but one paragraph where the term fictional is discussed.
And, similar to Ed, I doubt that "premise (1) is surely true".


Why do you post anonymously? Do you fear the thought police? This is not exactly a hot button topic. Anyway, good comment.

You write,
>>1. X
2. Necessarily, if X then Y.
3. So, necessarily, Y.

But this is invalid. Consider this argument:

3. It's raining today.
4. Necessarily, if it's raining today then the ground is wet.
5. So, necessarily, the ground is wet.<<

You are quite right about this. You have shown that an argument pattern in modal propositional logic is invalid. But my inference is of a different pattern, and involves quantification.

Can you provide a counterexample to it?

In any case, I am comfortable with strengthening (1) to 'Necessarily, Hamlet is an incomplete object.'

You say that someone could give a complete description of Hamlet. Well, God could, but not any finite novelist or story-teller, not even the Bard himself. For there are infinitely many properties, perhaps even continuum-many. You would have to specify all of Hamlet's relational properties and all their entailments for starters. When he gave his soliloquy, how far was he from the moon, and what were the exact contents of his GI tract, etc. ad infinitum?

The incompleteness of fictional objects is the mirror image of the finitude of the human mind.

Okay. So, more technically, your argument has the following structure:

1. Fx
2. [] (x)(Fx -> Gx)
3. [] Gx

Right? But, this is still invalid. Consider this argument:

4. I own a dog.
5. Necessarily, for any x, if x owns a dog then x owns a mammal.
6. So, necessarily, I own a mammal.

(4) and (5) are true, yet, (6) is false. So, the argument is invalid. We could fix the structure by making the first premise necessary. But, that would make it unsound.

Now, since this is the same structure of your argument, it, too, is invalid, unless we fix the first premise, which you said you're willing to do. But, I then claimed that the new premises was false; for someone could give a complete description of Hamlet. You respond by saying that only God could. Well, that's good enough, right? If God could do it, then it's true that someone could do it and, thus, it's not an impossible object.

But, I also think it's false that only God could do it. We could suppose there's a possible world in which the Bard is writing on a super-duper computer and, recognizing that he could never type out a complete description of Hamlet, he asks the computer to perform a supertask to do it. Now, of course, this depends on the possibility of supertasks, which you may deny. But, I don't. So, here we may be at an impasse.

Btw, I write anonymously out of insecurity. :-/

Thanks for blogging your thoughts. I really enjoy them!


Thanks for your comment. Did we meet in Prague in September? London Ed was there too. We Amis and Brits are pretty bad with languages, sad but true, due to our insularity.

Would you grant that when you are thinking about Hamlet there is a merely intentional object before your mind? After all, you are thinking of something, not nothing. Or do you hold that

1. I am thinking about x


2. There exists mind-independently an x such that I am thinking about x?


You're right! My argument as stated is invalid as I vaguely sensed as I was quickly composing it. Perhaps I was tacitly adding a necessity operator to (1).

So I cheerfully add the necessity operator to (1).

I also add the premises

0. Necessarily, for every x, if x is a fictum of a finite mind, then x is incomplete.


0*. Necessarily, Hamlet is a fictum of a finite mind, Shakespeare's.

And now I should think the argument is in the clear.

I think, now, that in order for your argument to work you need (0*) to work with per se necessity. However, I suspect that it's only working with per accidens necessity. That is, it seems that it might only be an accident of history that Hamlet is the product of Shakespeare. As I said in my previous comment, it seems like there's a possible world in which Shakespeare or somebody else writes Hamlet on a computer that's capable of performing a supertask that gives a complete description of Hamlet.

So, if all this is correct then the argument is still invalid since it equivocates on the word "necessarily." In (0*), it means per accidens necessity, but in the conclusion it means per se necessity.

Arizona Bill:
No, we haven´t, if you mean the Analytic theology meeting, I wasn´t there ...
To your question: I would say that it is very hard question. It reminds me of (I think) similar problem: we have some song. Was this song really invented, composed, or was it in fact only "discovered"?

Anyway, I am prone more to agree with reply 2. At least from the moment Hamlet was made up, he became mind-independent in a sense ...


>>That is, it seems that it might only be an accident of history that Hamlet is the product of Shakespeare.<<

I'm afraid that makes no sense to me. There is no Hamlet apart from Shakespeare's creative acts. That very character could not have been originated by anyone else. (This is of course consistent with there being Hamlet-like characters in other plays and novels by other writers.)

Did you know that there's a historian of logic in London who has invented a character with the unlikely name of 'Arizona Bill' who writes a philosophy blog from the Sonoran Desert in the USA.

I think there is something wrong with your arguments.

By my opinion, it is necessary to distinguish between objects and descriptions of objects. Hamlet is an object, Shakespeare play is a description of object.

So, according to this view, your sentence "Hamlet is an incomplete object" is wrong, because what is incomplete is description of Hamlet.

It is impossible to guess anything about existence of objects from incompleteness of theirs descriptions.

I think you should also take into account that every description of each physically existent object is incomplete. It is even impossible to give complete description of any physical objects (at least if we go on particle level).

So nothing existed ?

How do you know Richard III really existed ? You know about him only from books. And, according to your line of arguments, he is also "incomplete".

I dare to add small addendum yet.

We should consider two books:
A) Shakespeare's play about Hamlet.
B) Biography or even autobiography of some person, that really existed in the past.

Hamlet, as well as person B, are "incomplete" in sense of your proof, so they both should be imposible objects.
But Hamlet is fictional figure, person in B was real individual.

Your proof went to the wrong conclusion for situation B, so it must be wrong.

Hamlet is a mental creation by its finite author. This object is as incomplete as its description.

I have a question:

If I wrote a sentence "Charles is 180 cm tall", it means that such a person I wrote about is not possible individual, because he is incomplete ?

Obviously not. Don't confuse a description with what is described. If Charles is an actual individual, then he is completely determinate. But descriptions of him will typically be incomplete.

Person B is complete. Again, you seem to be confusing descriptions with what they describe.

I apologize that I wrote too much. Thanks for the answers, now I undestand you better.

But I still have some problems: it seems to me, that you distinguish between possible, but unactual, and fictional.
I undestand, that fictional is not possible - but there is a practical question: how do you know, what is and what is not "really" possible ? It is not actual, so you cannot use sense data. In both of the cases you have only descriptions, and they both are necessarily incomplete. From practical point of view, it is undistiguishable (if we leave aside probability), difference is only "ontological".

So, as it seems to me, that if we accept your conclusions, than every thought or written sentence in the form of "X is possible" must be a contradiction, because we were not able to include all the properties of X. So X is incomplete, according to you also impossible, and therefore the sentence is contradictory.

Maybe it is nonsense, but I would like to mention one idea:
I think for universals is also true, that "there is a property P such that x is indeterminate with respect to P".
If object with properties, ascribed to Hamlet, could be (hypothetically) actualized in many slightly different instances, than could it not be so that Shakespeare's hero is, in fact, a universal ?
If it is acceptable, than is it correct to say about some universal X that "X is possible" ? If yes, than why it could be wrong in principle to says just the same about Hamlet ?

About your third consideration: "It seems to be part of the very sense of the phrase 'fictional individual' that such individuals be, well, fictional, that is, irreal or unreal. ..."
"Fictional individual" is not the property of Hamlet, ascribed to him in the play. It is the fact of history.
So, I think, it is not the fact of the discourse, it is the fact of the metadiscourse. As such, it could not be used in proofs of possibility of Hamlet's actual existence.
I think "third consideration" is similar like to argue that some invented machine cannot be constructed, because invention is mental creation and thus immaterial.

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